For the anticipated application of quantum computing in electronic structure simulation, we propose a systematically improvable end-to-end pipeline to overcome the resource and noise limitations prevalent on developing quantum hardware. Using density matrix embedding theory as a problem decomposition technique, and an ion-trap quantum computer, we simulate a ring of 10 hydrogen atoms without freezing any electrons. On the most aggressive decomposition setting, the original 20-qubit system is divided into 10 two-qubit subproblems. Combining this decomposition with circuit optimization and density matrix purification, we are able to accurately reproduce the potential energy curve in agreement with the full configuration interaction energy in the minimal basis set. Although problem decomposition techniques are generally approximate methods, the induced error can often be systematically suppressed by increasing the size of the subproblems. This allows our pipeline to become applicable to more-complex systems as quantum computers grow in computational capacity. Our experimental results are an early step in demonstrating how the appropriate choice of decomposition could be a critical component for enabling the quantum simulation of larger, more industrially relevant molecules using fewer computational resources.
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